reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;
reserve O for Ordinal,
        R for right_zeroed add-associative right_complementable
          right_unital distributive non trivial doubleLoopStr,
        p for Polynomial of O, R;
reserve O for Ordinal,
        R for right_zeroed add-associative right_complementable
             right_unital distributive non trivial doubleLoopStr,
        p for Polynomial of O, R;

theorem Th40:
  for X be set, S be ZeroStr
    for p be Series of X,S, b be bag of X st b in Support p holds
       support b c= vars p
proof
  let X be set,S be ZeroStr;
  let p be Series of X,S, b be bag of X such that A1: b in Support p;
  set SS={support b where b is Element of Bags X:b in Support p};
  b in Bags X by PRE_POLY:def 12;
  then support b in SS by A1;
  then support b c= union SS by ZFMISC_1:74;
  hence thesis by Th39;
end;
